Research

I am a research scientist at the Uniformed Services University in Bethesda, Maryland. My research focuses on developing new analytical tools to facilitate understanding of dynamical processes that occur on networks. By realizing information theoretic analyses via nonparametric statistics, researchers can gain new insights into the organization of complex systems. A selection of my research interests are summarized below.

Computational Mechanics

Computational mechanics is a subdiscipline of the theory of stochastic processes motivated by finding the minimal representation of a stochastic process based on its predictive distribution. It is not this, and really warrants its own Wikipedia entry. For a good overview, see here, and here, while the course material still exists. An excellent review article is here.

The central object of study for computational mechanics is the causal or predictive states of the process, resulting from partitioning pasts of the process based on their predictive distributions, and the transitions between those states.

If the process you are interested is conditionally stationary, then you can learn its predictive states and the transitions between them from a (long enough) single realization of the process. One approach to this learning problem is Causal State Splitting Reconstruction.

Information Theory

Information theory provides a mathematical framework for describing how a system stores, processes, and transmits information. Developed by Claude Shannon in the 1940s to model communication channels, information theory has undergone a renaissance, finding applications in the physical, biological, and social sciences. My research focuses on developing new information theoretic measures that can be estimated from data, with an emphasis on methods applicable to dynamical systems.